Least Common Multiple (LCM) of 126 and 157
The least common multiple (LCM) of 126 and 157 is 19782.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 126 and 157?
First, calculate the GCD of 126 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 157 = 0 remainder 126 |
| 2 | 157 ÷ 126 = 1 remainder 31 |
| 3 | 126 ÷ 31 = 4 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 52 | 3172 |
| 110 and 76 | 4180 |
| 110 and 21 | 2310 |
| 57 and 189 | 3591 |
| 111 and 199 | 22089 |